Noise reducing method, noise reducing device, medium, and program

ABSTRACT

A noise reduction apparatus in accordance with the present invention is configured to reduce mosquito noise while retaining edges by calculating the maximum value Y of the difference values of adjacent pixels in an area of M×N around a notice pixel by using a difference value calculator  12  and a maximum value calculator  13,  by controlling a pixel replacement device  14  depending on Y and the difference value X from the notice pixel in the area of J×K narrower than the area of M×N, and by carrying out more intense smoothing depending on the magnitude of X with respect to Y, that is, when X is smaller than Y.

TECHNICAL FIELD

[0001] The present invention relates to a noise reduction method, anoise reduction apparatus, a medium and a program applicable todigitally compressed decoded images, for example.

BACKGROUND ART

[0002] In an image compression technology, such as MPEG, discrete cosinetransform (DCT) is used generally. Noise referred to as mosquito noiseoccurs in the decoded signals of video signals compressed on the basisof DCT. This is because high-frequency components are quantized roughlywhen image compression is carried out, whereby parts of high-frequencycomponents in blocks abundantly including high-frequency components arelost, and whereby information lost at the time of decoding cannot bedecoded, and high-frequency distortion (ringing) occurs. Hence, if aringing-like distortion occurs near image edges, particularly at theflat portions thereof, the distortion is detected as significantdeterioration.

[0003] As a method of reducing such mosquito noise without changingimage edges, a method disclosed in Japanese Laid-open Patent ApplicationNo. Hei 9-200759, for example, is available.

[0004] The entire disclosure of the above-mentioned publication isincorporated herein by reference in its entirety.

[0005] In this method, the gradient (for example, a difference value ofimage values of adjacent images in a predetermined area) of each DCTblock is calculated, and anisotropic diffusion is controlled on thebasis of it.

[0006] The anisotropic diffusion is a method wherein a threshold valueis set, and changes not more than the threshold value are smoothened,whereby minute noise reduction is carried out. According to JapaneseLaid-open Patent Application No. Hei 9-200759, a threshold value is setin each block depending on the gradient, whereby mosquito noisereduction is attained while edges are retained.

[0007]FIG. 9 is a block diagram showing a method using theabove-mentioned anisotropic diffusion. Herein, luminance signalprocessing is taken as an example and explained. In FIG. 9, numerals101, 105 and 112 designate 8-line line memory devices, numeral 102designates a selector, numerals 103, 104, 106 and 107 designate 1-lineline memory devices, numeral 108 designates a gradient calculator,numeral 109 designates a calculator for calculating a threshold valuefor controlling anisotropic diffusion depending on the threshold value,numeral 110 designates a random access memory device (RAM), which isreferred to when the threshold value is calculated, and numeral 111designates an anisotropic diffuser.

[0008] In this configuration, a video signal subjected to anisotropicdiffusion is input to the selector 102 via a path A0. Hence, theselector 102 switches between the signal once subjected to anisotropicdiffusion on the path A0 and a signal not subjected to anisotropicdiffusion on a path B0, and a series of anisotropic diffusion processesare carried out twice as fast as the dot clock of the video signal,whereby the anisotropic diffusion is carried out twice.

[0009] A decoded signal is input as a video input to the 8-line linememory device 101, the output of the line memory device 101 and a signalprocessed by the anisotropic diffuser 109 are input to the selector 102,and selection is carried out and a signal is output.

[0010] The line memory device 101 is used for temporary signal storagewhen the switching between the path A0 after the anisotropic diffusionand the video signal input path B0 is carried out.

[0011] The signal selected by the selector 102 is input to the linememory device 103, and its output is further input to the line memorydevice 104. The three line signals of the selector 102, the line memorydevice 103 and the line memory device 104 are input to the gradientcalculator 108.

[0012] The gradient calculator 108 calculates gradients by using thethree line signals and outputs the maximum value of the gradients in theDCT block. The threshold calculator 109 calculates the threshold valueby using the RAM 110 depending on the maximum value of the gradients inthe DCT block, that is, the output of the gradient calculator 108.

[0013] The output of the selector 102 is input to the 8-line line memorydevice 105, and its output is input to the anisotropic diffuser 111.This 8-line line memory device 105 is provided for positional adjustmentso that the threshold value calculated for the DCT block is used as thethreshold value for the anisotropic diffusion of the same DCT block.

[0014] The line memory device 106 delays the output of the line memorydevice 105 by one line and outputs it. The line memory device 107 delaysthe output of the line memory device 106 by further one line.

[0015] From the three line signals of the outputs of the line memorydevice 105, the line memory device 106 and the line memory device 107,the anisotropic diffuser 111 carries out anisotropic diffusion in theDCT block by using the threshold value calculated by the thresholdcalculator 109.

[0016] The output of the anisotropic diffuser 111 is input to theselector 102 via the path A0 and the line memory device 112. The linememory device 112 is used as a temporary storage memory device andoutputs only the signal subjected to anisotropic diffusion twice.

[0017] In the method of using anisotropic diffusion, only the adjacentpixels are used as pixels contributing to the diffusion. Furthermore, inorder to set a conduction value for determining the degree of smoothingin stable conditions so that the effect of noise reduction is enhancedwhile retaining image edges, and in order to obtain a high effect, aplurality of attempts are necessary.

[0018] In the method disclosed in Japanese Laid-open Patent ApplicationNo. Hei 9-200759, depending on the difference value from the adjacentpixels, the degree of smoothing in the case when the difference value issmall is changed greatly from that in the case when the difference valueis large, whereby a high noise reduction effect is obtained by carryingout two attempts.

[0019] With this configuration, when the gradient is large in each DCTblock, the threshold value is made larger and a high degree of smoothingis carried out. On the other hand, when the gradient is small, thethreshold value is made smaller and a low degree of smoothing can becarried out.

[0020] As a result, in a block having small high-frequency components,the threshold value for anisotropic diffusion is made smaller, and afine image is stored.

[0021] In addition, in a block having large high-frequency components, alarge degree of smoothing is carried out, whereby mosquito noisereduction can be attained while retaining image edges.

[0022] However, in the method of reducing mosquito noise by using theinformation of the DCT blocks as described above, it is necessary toreceive the positional information of the DCT blocks from a decoder, forexample.

[0023] In the case of a decoder in a generally widespread DVD player orthe like, however, only a decoded image signal is transmitted usually,but the positional information of the DCT blocks is not transmitted.

[0024] Hence, in the case when the positional information of the DCTblocks is not obtained, the above-mentioned conventional method has aproblem of being unable to carry out noise reduction.

[0025] Furthermore, there is also a problem of being unable to carry outnoise reduction for an image signal that is subjected to an expansion orcompression process wherein no DCT blocks are retained.

[0026] Still further, in the method of using anisotropic diffusion,numerous multipliers are used, and attempts must be repeated a pluralityof times to obtain an effect, thereby causing a problem of makinghardware very complicated.

DISCLOSURE OF THE INVENTION

[0027] An object of the present invention is to provide a noisereduction method, a noise reduction apparatus, a medium and a programcapable of reducing noise while retaining image edges without usinginformation obtained at the time of compression, such as DCT blocks, andwithout requiring conventional complicated hardware.

[0028] The 1st invention of the present invention corresponding toclaim 1) is a noise reduction method for the decoded signal of adigitally compressed image signal, comprising:

[0029] a gradient calculation step of obtaining a predetermined gradientin an area of vertical M×horizontal N pixels (M and N are positiveintegers) around a notice pixel,

[0030] a difference value calculation step of calculating, in an area ofvertical J×horizontal K pixels (J and K are positive integers satisfyingthe relationships of J≦M and K≦N, respectively) around said noticepixel, (J×K−1) difference values between said notice pixel and pixelsother than said notice pixel,

[0031] a correction value calculation step of calculating correctionvalues from said gradient obtained by said gradient calculation step andsaid (J×K−1) difference values obtained by said difference valuecalculation step, and

[0032] an addition step of calculating a new notice pixel by adding saidcorrection values to said notice pixel.

[0033] With this method, mosquito noise reduction can be carried outwithout using information obtained at the time of compression, such asDCT blocks, and without requiring complicated hardware.

[0034] The 7th invention of the present invention (corresponding toclaim 7) is a noise reduction apparatus for the decoded signal of adigitally compressed image signal, comprising:

[0035] gradient calculation means of obtaining a predetermined gradientin an area of vertical M×horizontal N pixels (M and N are positiveintegers) around a notice pixel,

[0036] difference value calculation means of calculating, in an area ofvertical J×horizontal K pixels (J and K are positive integers satisfyingthe relationships of J≦M and K≦N, respectively) around said noticepixel, (J×K−1) difference values between said notice pixel and pixelsother than said notice pixel, correction value calculation means ofcalculating correction values from said gradient obtained by saidgradient calculation means and said (J×K−1) difference values obtainedby said difference value calculation means, and

[0037] addition means of calculating a new notice pixel by adding saidcorrection values to said notice pixel.

[0038] With this configuration, mosquito noise reduction can be carriedout without using information obtained at the time of compression, suchas DCT blocks, and without requiring complicated hardware.

[0039] The 13th invention of the present invention (corresponding toclaim 13) is a noise reduction apparatus for the decoded signal of adigitally compressed image signal, comprising:

[0040] gradient calculation means of obtaining a predetermined gradientin an area of vertical M×horizontal N pixels (M and N are positiveintegers) around a notice pixel,

[0041] difference value calculation means of calculating, in an area ofvertical J×horizontal K pixels (J and K are positive integers satisfyingthe relationships of J<=M and K<=N, respectively) around said noticepixel, (J×K−1) difference values between said notice pixel and pixelsother than said notice pixel,

[0042] filter coefficient calculation means of calculating filtercoefficient from said gradient obtained by said gradient calculationmeans and said (J×K−1) difference values obtained by said differencevalue calculation means, and

[0043] filtering means of carrying out filtering on the basis of saidcalculated filter coefficients.

[0044] With this configuration, mosquito noise reduction can be carriedout without using information obtained at the time of compression, suchas DCT blocks, and without requiring complicated hardware.

[0045] The 19th invention of the present invention (corresponding toclaim 19) is a medium holding a program and/or data for carrying out theoperations of all or part of the steps of said noise reduction method inaccordance with the 1st invention by using a computer and beingprocessable by the computer.

[0046] The 20th invention of the present invention (corresponding toclaim 20) is a medium holding a program and/or data for carrying out thefunctions of all or part of the means of said noise reduction apparatusin accordance with the 7th or 18th inveniton by using a computer andbeing processable by the computer.

[0047] The 21st invention of the present invention (corresponding toclaim 21) is a program for causing a computer to carry out all or partof said gradient calculation step, said difference value calculationstep, said correction value calculation step and said addition step ofsaid noise reduction apparatus in accordance with the 1st invention.

[0048] The 22nd invention of the present invention (corresponding toclaim 22) is a program for activating a computer as all or part of saidgradient calculation means, said difference value calculation means,said correction value calculation means and said addition means of saidnoise reduction apparatus in accordance with the 7th or 13th invention.

BRIEF DESCRIPTION of DRAWING

[0049]FIG. 1 is a flowchart showing a noise reduction method inaccordance with a first embodiment of the present invention;

[0050]FIG. 2 is a view showing a graph for illustrating calculationexamples of the absolute value of a correction value AA;

[0051]FIG. 3 is a block diagram showing the configuration of a noisereduction apparatus in accordance with a second embodiment of thepresent invention;

[0052]FIG. 4 is a block diagram showing an example of the configurationof a pixel replacement device shown in FIG. 3;

[0053]FIG. 5 is a view showing a graph for illustrating examples of datastored in RAM shown in FIG. 3;

[0054]FIG. 6 is a block diagram showing the configuration of a noisereduction apparatus in accordance with a third embodiment of the presentinvention;

[0055]FIG. 7 is a block diagram showing an example of the configurationof an adaptive filtering device shown in FIG. 6;

[0056]FIG. 8 is a view showing a graph for illustrating examples of datastored in RAM shown in FIG. 6; and

[0057]FIG. 9 is the block diagram showing the configuration of theconventional mosquito noise apparatus.

EXPLANATIONS OF NUMERALS

[0058] 12, 32, 52, 72 difference calculators

[0059] 13, 53 maximum calculators

[0060] 14 pixel replacement device

[0061] 35 correction value calculator

[0062] 37, 77 format detector

[0063] 39, 79 controller

[0064] 54 adaptive filtering device

[0065] 75 filter coefficient calculator

[0066] 76 filtering device

BEST MODE FOR CARRYING OUT THE INVENTION

[0067] Embodiments of the present invention will be described belowreferring to the drawings.

[0068] In the following explanation, digitized data is used as an inputvideo signal; “horizontal” represents the horizontal direction of ascreen displayed as one frame; “vertical” represents the verticaldirection of the screen displayed as one frame; and one line representsone horizontal scanning period.

[0069] (1) First embodiment

[0070]FIG. 1 is a flowchart illustrating a first embodiment of a noisereduction method in accordance with the present invention.

[0071] In this embodiment, an explanation is given with respect to anexample wherein M and N for determining the range for obtaining themaximum value (corresponding to “the predetermined gradient” of thepresent invention) of the difference values among pixels around a noticepixel are 15, and J and K for determining a pixel range for obtainingnew pixel values are 3, furthermore a luminance signal is used as avideo signal input.

[0072] First, at step S1, the difference values of the luminance valuesamong the adjacent pixels in the whole area of 15×15 pixels around thenotice pixel are calculated.

[0073] At step S2, the maximum value YA of the absolute values of thedifference values among the adjacent pixels in the area of 15×15 pixels,calculated at step S1, is calculated.

[0074] At step S3, the difference values between the luminance value ofthe notice pixel and the luminance values of the other pixels in thearea of 3×3 around the notice pixel are calculated. The differencevalues are assumed to be XA1, XA2, . . . , XA8. The signs of XA1, XA2, .. . , XA8 are assumed to be positive when the luminance value of thenotice pixel is larger than or equal to the luminance values of thepixels other than the notice pixel, and assumed to be negative when theluminance value is smaller.

[0075] At step S4, correction values AAk (k=1, 2, . . . , 8) areobtained by using YA calculated at step S2 and XAk (k=1, 2, . . . , 8)calculated at step S3. In other words, correction values AA1, AA2, . . ., AA8, wherein there are correspondences such that-the value AA1 iscalculated from YA and XA1, the value AA2 is calculated from YA and XA2,and so on, are obtained. The actual method of obtaining the correctionvalues will be described later (see FIG. 2).

[0076] Next, at step S5, the correction values AA1, AA2, . . . , AA8obtained at step S4 are added, and the result is assumed to be DA.

[0077] At step S6, the absolute value of DA is compared with a set valueLA; when the absolute value of DA is smaller than the set value LA, thesequence advances to step S7, and the value of DA is used as an additionvalue EA. When the absolute value is equal to or larger than the setvalue LA, the sequence advances to step S8, and the set value LA is usedas the addition value EA while the sign of the set value LA is madeidentical to that of DA.

[0078] The set value LA will be described later.

[0079] At step S9, the luminance value of the notice pixel is added toEA obtained at step S7 or S8, whereby a new notice pixel is obtained andoutput in place of the notice pixel.

[0080] At step 10, a judgment as to whether the processing for pixels tobe subjected to pixel replacement is completed or not; if the processingis not completed, the sequence from step S1 to step S9 is repeated whilethe pixel not subjected to the processing is used as the notice pixel.

[0081] If the processing is completed, the processing ends.

[0082] The gradient calculation step of the present inventioncorresponds to steps S1 to S2. In addition, the difference valuecalculation step of the present invention corresponds to step S3.Furthermore, the correction value calculation step of the presentinvention corresponds to steps S4 to S8. Still further, the additionstep of the present invention corresponds to step S9.

[0083] Herein, as mentioned above, the method of obtaining thecorrection values will be described below.

[0084] In other words, for example, when the absolute values of XA1,XA2, . . . , XA8 are smaller than YA in the above-mentionedconfiguration, the correction values AA1, AA2, . . . , AA8 are set sothat the luminance value of the notice pixel is close to the luminancevalues of the adjacent pixels. Hence, the minute changes near edges canbe made smooth.

[0085] In addition, when the values of XA1, XA2, . . . , XA8 are closeto YA, the correction values AA1, AA2, . . . , AA8 are set at smallvalues. The reason why the correction values are herein set at smallvalues will be described further later.

[0086] Furthermore, EA is limited by using the set value LA, wherebymosquito noise reduction can be attained while retaining edges.

[0087] The above-mentioned matters will be described as followsreferring to FIG. 2. Herein, FIG. 2 is a graph illustrating the methodof calculating the absolute values of the correction values. As shown inthe figure, a graph for the calculation of the correction values isdetermined beforehand for each of the maximum values of the differencevalues; however, all the graphs have a similar characteristic.

[0088] As shown in FIG. 2, for example, setting is done beforehand sothat the absolute value of the correction value AA1 (when k=1) becomeslarger as an evaluation value (the value corresponding to the abscissaof FIG. 2) obtained from the equation defined by (Equation 1) becomeslarger up to a threshold value TA1, and so that the absolute valuebecomes smaller as the above-mentioned evaluation value becomes largerthan a threshold value TA2. Herein, the signs of AA1, AA2, . . . , AA8correspond to those of XA1, XA2, . . . , XA8, respectively. In(Equation 1) , AA1, AA2, . . . , AA8 are represented by AAk (k=1, 2, . .. , 8), and XA1, XA2, . . . , XA8 are represented by XAk (k=1, 2, . . ., 8).

[0089] The method of obtaining the above-mentioned correction valueswill be described further with respect to its effect.

[0090] When the above-mentioned evaluation value is smaller than thethreshold value TA1 (about 0.3), an edge portion existing in the area of15×15 pixels is outside the area of 3×3 pixels. Hence, in this case, asdescribed above, the correction value is determined so that theluminance value of the notice pixel in the area of 3×3 pixels becomesclose to the luminance values of the adjacent pixels, whereby smoothingcan be carried out securely in areas other than the area including theedge.

[0091] On the other hand, when the above-mentioned evaluation valueexceeds the threshold value TA2 (in other words, when the differencevalue XAk is close to the maximum value YA), it is highly possible thatan edge portion existing in the area of 15×15 pixels is inside the areaof 3×3 pixels. Hence, in this case, it is supposed that the edge can beretained essentially by not correcting the notice pixel. In actualpractice, however, when the above-mentioned evaluation value exceeds thethreshold value TA1, if the correction value is set abruptly at 0, thecorrection value is changed abruptly, thereby causing new noise on thecontrary.

[0092] For this reason, in the present invention, the correction valueis not set abruptly at 0 even when the above-mentioned evaluation valueexceeds the above-mentioned threshold value TA1, but the correctionvalue is set so as to be retained at the same value in the range betweenthe threshold values TA1 to TA2 and so as to become gradually close to 0as the evaluation value exceeds the threshold value TA2 as shown in FIG.2.

[0093] In this way, no new noise occurs, whereby mosquito noise can bereduced securely while retaining edges. $\begin{matrix}{{{\frac{{XAk}}{({YAk})^{n}}1} \leq n \leq 2},\quad {k = 1},2,\ldots \quad,8} & \left( {{Equation}\quad 1} \right)\end{matrix}$

[0094] In the present invention, the processing is carried out aroundthe notice pixel; therefore, the method of replacing pixels is attainedby a simple configuration comprising only an adder, regardless of theinformation at the time of compression, such as DCT blocks.

[0095] When 8-bit data, that is, 256-level data, is used, the set valueLA is preferably 2 or more and 16 or less, and further preferably 4 ormore and 8 or less.

[0096] The set value LA determines the maximum value of the absolutevalues of the correction values with respect to the notice pixel. Byincreasing this value, the correction values can be calculated inaccordance with the calculations at steps S1 to S5. However, the maximumvalue of the correction values required for noise reduction is notlarger than the values calculated at step S1 to step S5 in some cases.Setting a correction value larger than a necessary value is meaninglessand exerts an influence of reducing the effect of edge retaining. Hence,by setting LA at an appropriate value, it is possible to obtain aneffect of preventing this problem.

[0097] In addition, the calculations of obtaining AA1, AA2, . . . , AA8from YA and XA1, XA2, . . . , XA8 may be the same calculations,respectively, for example; furthermore, the calculations may bedifferent in the horizontal, vertical and slanting directions from thenotice pixel; still further, calculations wherein values become largerrelatively as the distance is closer depending on the distance from thenotice pixel may also be used; besides, the calculations are not limitedto these.

[0098] Furthermore, in this embodiment, an example wherein the maximumvalue of the absolute values of the difference values of the luminancevalues among the adjacent pixels is used as the predetermined gradientof the present invention is described; however, the gradient is notlimited to this. The above-mentioned predetermined gradient may be thesecond largest value in the absolute values of the difference values ofthe luminance values among the adjacent pixels, for example; or aplurality of values may be selected in the decreasing order of theabsolute values of the difference values of the luminance values amongthe adjacent pixels, beginning from the maximum value, and the averagevalue of the values may be obtained, but the gradient is not limited tothis.

[0099] Still further, in this embodiment, an example wherein theluminance signal is used as the video signal input is described;however, the input signal is not limited to this; for example, a colordifference signal may be used as the input signal; furthermore, theluminance signal may be used at step S1 and step S2, and the colordifference signal at the same position may be used at step S3 to stepS11; however, the input signal is not limited to these.

[0100] Moreover, examples wherein M and N are 15, and J and K are 3 aredescribed; however, their values are not limited to these.

[0101] (2) Second embodiment

[0102]FIG. 3 is a block diagram showing the configuration of a mosquitonoise reduction apparatus in accordance with an embodiment of the noisereduction apparatus of the present invention.

[0103] In this embodiment, an explanation is given with respect to anexample wherein M and N for determining the range for obtaining themaximum of the difference value among pixels around a notice pixel are15, and J and K for determining a pixel range for obtaining new pixelvalues to be replaced are 3, furthermore, a luminance signal is used asthe video signal input.

[0104] In FIG. 3, numeral 11 designates a line memory device fordelaying an input signal by 14 lines, numeral 12 designates a differencevalue calculator for calculating differences among the horizontal andvertical adjacent pixels in a predetermined area, numeral 13 designatesa maximum value calculator, numeral 14 designates a pixel replacementdevice, and numeral 15 designates a line memory device for delaying theinput signal by eight lines. In the mosquito noise reduction apparatusconfigured as described above, its operation will be described below.

[0105] A decoded signal is input as a video input to the line memorydevice 11 and the line memory device 15. The line memory device 11delays the input video signal by 14 lines and outputs 15 line signals intotal including the input signal to the difference value calculator 12.To the image replacement device 14, the line memory device 15 outputsthree line signals centered at a line delayed by seven lines withrespect to the input signal.

[0106] The difference value calculator 12 receives 15 line signals fromthe line memory device 11, uses a pixel delayed by seven lines withrespect to the input video signal and delayed by seven pixels withrespect to the input of the difference value calculator 12 as a noticepixel, calculates the difference values among the adjacent pixels in thehorizontal and vertical directions in all the pixels in the area of15×15 pixels around the notice pixel, and outputs all the differencevalues to the maximum value calculator 13.

[0107] The maximum value calculator 13 obtains the maximum value of theabsolute values of the difference values in the area of 15×15 from thedifference values among the adjacent pixels, which are output from thedifference value calculator 12, and outputs it to the pixel replacementdevice 14.

[0108] By using signals in the area of 3×3 pixels around the noticepixel and on the basis of the output of the maximum value calculator 13around the notice pixel determined by the difference value calculator12, the pixel replacement device 14 calculates a new notice pixel forthe signals delayed by six lines, seven lines and eight lines withrespect to the input video signal, that is, the output of the linememory device 15, and outputs the new notice pixel in place of thenotice pixel.

[0109] This pixel replacement device 14 will be described in detailreferring to FIG. 4.

[0110]FIG. 4 is a block diagram showing a configuration example of thepixel replacement device. In FIG. 4, numerals 31 and 33 designate delaydevices, numeral 32 designates a difference value calculator, numeral 34designates RAM used as a lookup table for calculating correction values,numeral 35 designates a correction value calculator, numeral 36designates an adder, numeral 37 designates a format detector, numeral 39designates a controller for rewriting the content of the RAM 34 inaccordance with the result of format detection, numeral 38 designatesread-only memory (ROM) referenced by the controller 39.

[0111] The correction value calculation means of the present inventioncorresponds to the correction value calculator 35 and the like, and theaddition means of the present invention corresponds to the adder 36.

[0112] Input signals FB, GB and HB shown in FIG. 4 are signals delayedby six lines, seven lines and eight lines, respectively, with respect tothe video signal input shown in FIG. 3 among the output signals of theline memory device 15. In addition, an input signal IB corresponds tothe output from the maximum value calculator 13 of FIG. 3.

[0113] In the pixel replacement device configured as described above,its operation will be described below.

[0114] The three line signals of the inputs FB, GB and HB are inputsimultaneously to the delay device 31. From the delay device 31, ninesignals, that is, a no-delay signal, a one-pixel delay signal and atwo-pixel delay signal formed for each of the three line signals, areoutput. These correspond to the nine pixels in the area of 3×3, and itscenter, that is, the output signal obtained by delaying the input signalfrom the input GB by delay device 31, corresponds to the notice pixel.

[0115] The output from the delay device 31 is input to the differencevalue calculator 32, and the difference value calculator 32 calculatesthe difference values between the notice pixel and the eight outputs ofthe delay device 31 other than the notice pixel, and outputs them. Theoutputs of the difference value calculator 32 and the input IB are inputto the correction value calculator 35. The correction value calculator35 calculates eight correction values by using the RAM 34 depending onthe magnitudes of the input IB and the eight difference valuescalculated by the difference value calculator 32, and these are added.

[0116] When the absolute value of the result of the addition is largerthan a set value LB, the value of the set value LB, the sign of which isthe same as that of the result of the addition, is output; when theabsolute value is smaller than the set value LB, the result of theaddition is output.

[0117] The input GB is input to the delay device 33 having the samedelay as the total delay required for the difference value calculator 32and the correction value calculator 35, and its output is added to thenotice pixel and the output of the correction value calculator 35 by theadder 36, whereby the notice pixel is replaced with the new noticepixel.

[0118] Furthermore, correction value data to be stored in the ROM 38 isselected by the controller 39 depending on the video format detected bythe format detector 37. Then, other correction value data in the RAM 34is rewritten by the selected new correction value data, whereby it ispossible to have a correction value best suited for each format. Forexample, when the input signal is a video signal, real-time operationcan be carried out by transferring data stored in the ROM 38 to the RAM34 in a vertical retrace period.

[0119] With this configuration, for example, when the difference valuesin the area of 3×3 pixels are smaller than the maximum value of thedifference values in the area of 15×15 pixels around the notice pixel,setting is done so as to output correction values so that the pixelvalue of the notice pixel becomes close to the pixel values of theadjacent pixels, and the notice pixel is replaced with the new noticepixel, whereby the minute changes near the edges can be made smooth.

[0120] Furthermore, when the difference values in the area of 3×3 pixelsare larger, small correction values are set, and the correction valuesare limited by using the set value LB, whereby mosquito noise reductioncan be attained while retaining the edges.

[0121] Still further, in order to carry out processing around the noticepixel, only the adder is used for the calculation of the pixelreplacement device, regardless of the information at the time ofcompression, such as DCT blocks, whereby the hardware can be configuredsimply.

[0122] When 8-bit data, that is, 256-level data, is used, the set valueL is preferably 2 or more and 16 or less, and further preferably 4 ormore and 8 or less.

[0123] When the maximum value of the difference values in an area of M×Nis assumed to be YB and the typical value of the difference valuesbetween the notice pixel and pixels other than the notice pixel in anarea of J×K is assumed to be XB, it is desirable that the correctionvalue to be set in the RAM 34 becomes larger as the value of (Equation2) becomes larger up to a threshold value TB, and that the correctionvalue becomes smaller as the value of (Equation 2) exceeds the thresholdvalue TB.

[0124] Moreover, it is further desirable that the correction value to beset in the RAM 34 is calculated from the following (Equation 3), and itis further desirable that n in (Equation 3) is 1.2 or more and 1.3 orless. $\begin{matrix}{{\frac{{XB}}{{YB}^{n}}1} \leq n \leq 2} & \left( {{Equation}\quad 2} \right)\end{matrix}$

$\begin{matrix}{{{{\exp \left\lbrack {{- A} \cdot \left( \frac{{XB}}{{YB}^{n}} \right)^{\gamma}} \right\rbrack} \cdot X \cdot S}\quad \begin{matrix}{A > 0} \\{2 \leq \gamma \leq 8} \\{1 \leq n \leq 2}\end{matrix}\quad 0}\quad < S \leq \frac{1}{\left( {J \times K} \right) - 1}} & \left( {{Equation}\quad 3} \right)\end{matrix}$

[0125] All the data to be set in the RAM may have the same values, forexample; the values may be different in the horizontal, vertical andslanting directions from the notice pixel; and the values may bedifferent depending on the distance from the notice pixel; besides, thevalues are not limited to these.

[0126] In addition, in this embodiment, the line memory device 11 andthe line memory device 15 are indicated independently; however, thesemay be united, whereby 15 line signals may be output to the differencevalue calculator 12 and three line signals may be output to the pixelreplacement device 14.

[0127] Furthermore, an example wherein the luminance signal is used asthe video signal input is described; however, a color difference signalmay be used as the input signal, the luminance signal may be used as theinput of the line memory device 11, and the color difference signal atthe same position of the luminance signal may be used as the input ofthe line memory device 15; however, the input signals are not limited tothese.

[0128] Moreover, examples wherein M and N are 15, and J and K are 3 aredescribed; however, their values are not limited to these.

[0129] Furthermore, the controller 39 is explained by taking theconfiguration for carrying out control depending on the result of theformat detector 37 as an example; however, for example, the controllermay be configured so as to carrying out control depending on the noiselevel of the input video; but the configurations are not limited tothese.

[0130] Furthermore, in this embodiment, an example wherein the maximumvalue of the absolute values of the difference values of the luminancevalues among the adjacent pixels is used as the predetermined gradientof the present invention is described; however, the gradient is notlimited to this. The above-mentioned predetermined gradient may be thesecond largest value in the absolute values of the difference values ofthe luminance values among the adjacent pixels, for example; or aplurality of values may be selected in the decreasing order of theabsolute values of the difference values of the luminance values amongthe adjacent pixels, beginning from the maximum value, and the averagevalue of the values may be obtained, but the gradient is not limited tothis.

[0131] Moreover, in this embodiment, the case wherein the set value LAis fixed is explained; however, for example, the set value may becontrolled depending on the noise level of the input video signal, butthe set value is not limited to this.

[0132] (3) Third embodiment

[0133]FIG. 6 is a block diagram showing the configuration of a mosquitonoise reduction apparatus in accordance with an embodiment of the noisereduction apparatus of the present invention.

[0134] In this embodiment, an explanation is given with respect to anexample wherein M and N are 15, J is 3, K is 5, and a luminance signalis used as the video signal input.

[0135] In FIG. 6, numeral 51 designates a line memory device fordelaying an input signal by 14 lines, numeral 52 designates a differencevalue calculator for calculating differences among the horizontal andvertical adjacent pixels in a predetermined area, numeral 53 designatesa maximum value calculator, numeral 54 designates an adaptive filteringdevice, and numeral 55 designates a line memory device for delaying theinput signal by eight lines.

[0136] In the mosquito noise reduction apparatus configured as describedabove, its operation will be described below.

[0137] A decoded signal is input as a video input to the line memorydevice 51 and the line memory device 55. The line memory device 51delays the input video signal by 14 lines and outputs 15 line signals intotal including the input signal to the difference value calculator 52.To the adaptive filtering device, the line memory device 55 outputsthree line signals centered at a line delayed by seven lines withrespect to the input signal.

[0138] The difference value calculator 52 receives 15 line signals fromthe line memory device 51, uses a pixel delayed by seven lines withrespect to the input video signal and delayed by seven pixels withrespect to the input of the difference value calculator 52 as a noticepixel, and outputs the difference values among the adjacent pixels inthe horizontal and vertical directions in all the pixels in the area of15×15 pixels around the notice pixel to the maximum value calculator 53.

[0139] The maximum value calculator 53 obtains the maximum value of theabsolute values of the difference values in the area of 15×15 from thedifference values among the adjacent pixels, which are output from thedifference value calculator 52, and outputs it to the adaptive filteringdevice 54.

[0140] On the basis of signals in the area of 3×5 pixels around thenotice pixel and the output of the maximum value calculator 53, theadaptive filtering device 54 carries out adaptive filtering for thesignals delayed by six lines, seven lines and eight lines with respectto the input video signal, that is, the output of the line memory device55.

[0141] This adaptive filtering device 54 will be described below indetail.

[0142]FIG. 7 is a block diagram of the adaptive filtering device 54. InFIG. 7, numerals 71 and 73 designate delay devices, numeral 72designates a difference value calculator, numeral 74 designates RAM usedas a lookup table for calculating filter coefficients, numeral 75designates a filter coefficient calculator, numeral 76 designates afiltering apparatus, numeral 77 designates a format detector, numeral 79designates a controller for rewriting the content of the RAM 74 inaccordance with the result of format detection, numeral 78 designatesROM referenced by the controller 79.

[0143] Input signals FC, GC and HC shown in FIG. 7 are signals delayedby six lines, seven lines and eight lines, respectively, with respect tothe video signal input shown in FIG. 6 among the output signals of theline memory device 51. In addition, an input signal IC corresponds tothe output from the maximum value calculator 53 of FIG. 6.

[0144] In the adaptive filtering device configured as described above,its operation will be described below.

[0145] The three line signals of the input signals FC, GC and HC areinput simultaneously to the delay device 71. From the delay device 71,15 signals, that is, a no-delay signal, a one-pixel delay signal, atwo-pixel delay signal, a three -pixel delay signal and a four-pixeldelay signal formed for each of the three line signals, are output.These correspond to the 15 pixels in the area of 3×5, and its centercorresponds to the notice pixel.

[0146] The output from the delay device 71 is input to the differencevalue calculator 72, and the difference value calculator 72 calculatesthe difference values between the notice pixel and the 14 outputs of thedelay device 71 other than the notice pixel, and outputs them.

[0147] The outputs of the difference value calculator 72 and the inputIC are input to the filter coefficient calculator 75. The filtercoefficient calculator 75 reads the values of the RAM 74 correspondingto the 14 difference values calculated by difference value calculator72, thereby calculating 14 filter coefficient candidates.

[0148] These 14 filter coefficient candidates correspond to the filtercoefficients of the 14 pixels other than the notice pixel, respectively.

[0149] In addition, the filter coefficient candidates are classifieddepending on the distance from the notice pixel; for example, the filtercoefficients in areas other than the area of 3×3 around the notice pixelare re-calculated so as to be not more than all the coefficient valuesin the area of 3×3 around the notice pixel, and become filtercoefficients corresponding to the 14 pixels, respectively; furthermore,the filter coefficient of the notice pixel is calculated so that one isobtained when the coefficient is added to all the filter coefficients ofthe 14 pixels and that of the notice pixcel, and the filter coefficientscorresponding to the 15 pixels are output to the filtering device 76.

[0150] An input E2 is input to the delay device 73 having the same delayas the total delay required for the difference value calculator 72 andthe filter coefficient calculator 75, and its output is filtered by thefiltering device 76 by using the filter coefficients of the 15 pixels,that is, the outputs of the filter coefficient calculator 75, and thenoutput.

[0151] Furthermore, data to be stored in the ROM 78 is selected by thecontroller 79 depending on the video format detected by the formatdetector 77, and the data in the RAM 74 is rewritten, whereby it ispossible to have a correction value best suited for each format.

[0152] For example, when the input signal is a video signal, real-timeoperation can be carried out by transferring data stored in the ROM 78to the RAM 74 in a vertical retrace period.

[0153] With this configuration, for example, when the difference valuesin the area of 3×5 pixels are smaller than the maximum value of thedifference values in the area of 15×15 pixels around the notice pixel,smoothing the minute changes near the edges are intensified byincreasing 14 filter coefficients other than that of the notice pixel,whereby mosquito noise can be reduced.

[0154] Furthermore, when the difference values in the area of 3×5 pixelsare larger than the maximum value of the difference values in the areaof 15×15 pixels, smoothing is weakened by decreasing the 14 filtercoefficients other than that of the notice pixel, whereby mosquito noisereduction can be attained while retaining the edges.

[0155] Still further, in order to carry out processing around the noticepixel, the adaptive filtering is carried out in the area of 3×5 pixels,for example, regardless of the information at the time of compression,such as DCT blocks, whereby a highly effective filtering effect can beattained by one attempt and the hardware is made simple.

[0156] When 8-bit data, that is, 256-level data, is used, and when themaximum value of the difference values in the area of 15×15 is assumedto be YC and the typical value of the difference values between thenotice pixel and pixels other than the notice pixel in the area of 3×5is assumed to be XC, it is desirable that the data to be set in the RAM34 decreases monotonously in accordance with (Equation 4) as shown inFIG. 8, for example, and it is also desirable that the data iscalculated by the following (Equation 5). $\begin{matrix}{{\frac{{XC}}{{YC}^{n}}1} \leq n \leq 2} & \left( {{Equation}\quad 4} \right)\end{matrix}$

$\begin{matrix}{{{{\exp \left\lbrack {{- A} \cdot \left( \frac{{XC}}{{YC}^{n}} \right)^{\gamma}} \right\rbrack} \cdot S}\quad \begin{matrix}{A > 0} \\{2 \leq \gamma \leq 8} \\{1 \leq n \leq 2}\end{matrix}\quad 0}\quad < S \leq \frac{1}{\left( {J \times K} \right) - 1}} & \left( {{Equation}\quad 5} \right)\end{matrix}$

[0157] All the data to be set in the RAM may have the same values, forexample; the values may be different in the horizontal, vertical andslanting directions from the notice pixel; and the values may bedifferent depending on the distance from the notice pixel; besides, thevalues are not limited to these.

[0158] In this embodiment, the line memory device 51 and the line memorydevice 55 are indicated independently; however, these may be united,whereby 15 line signals may be output to the difference value calculator52 and three line signals may be output to the adaptive filtering device54.

[0159] Furthermore, an example wherein the luminance signal is used asthe video signal input is described; however, a color difference signalmay be used as the input signal, the luminance signal may be used as theinput of the line memory device 51, and the color difference signal atthe same position of the luminance signal may be used as the input ofthe line memory device 55; however, the input signals are not limited tothese.

[0160] Moreover, examples wherein M and N are 15, J is 3 and K is 5 3are described; however, their values are not limited to these.Furthermore, the controller 79 is explained by taking the configurationfor carrying out control depending on the result of the format detector77 as an example; however, for example, the controller may be configuredso as to carrying out control depending on the noise level of the inputvideo; but the configurations are not limited to these.

[0161] Furthermore, in this embodiment, an example wherein the maximumvalue of the absolute values of the difference values of the luminancevalues-among the adjacent pixels is used as the predetermined gradientof the present invention is described; however, the gradient is notlimited to this. The above-mentioned predetermined gradient may be thesecond largest value in the absolute values of the difference values ofthe luminance values among the adjacent pixels, for example; or aplurality of values may be selected in the decreasing order of theabsolute values of the difference values of the luminance values amongthe adjacent pixels, beginning from the maximum value, and the averagevalue of the values may be obtained, but the gradient is not limited tothis.

[0162] In the above-mentioned embodiment, the case wherein the noticepixel addition process (step S9) is carried out for all pixels isdescribed; however, the embodiment is not limited to this; for example,the notice pixel addition process (step S9) may be carried out only whenthe absolute value of the difference value XAk (k=1, 2, . . . , 8) issmaller than the above-mentioned predetermined gradient (for example,YA), in other words, only when the evaluation value is the thresholdvalue TA1 or TA2 or less referring to FIG. 2, and the notice pixeladdition process may not be carried out in other cases.

[0163] Furthermore, the present invention is a program that carries outthe functions of all or part of the means (or apparatuses, devices,circuits, portions, etc.) of the above-mentioned noise reductionapparatus of the present invention by using a computer and operates incooperation with the computer.

[0164] Still further, the present invention is a program that carriesout the operations of all or part of the steps (or processes,operations, actions, etc.) of the above-mentioned noise reduction methodof the present invention by using a computer and operates in cooperationwith the computer.

[0165] Still further, the present invention is a medium that holds aprogram and/or data for carrying out all or part of the operations ofall or part of the steps of the above-mentioned noise reduction methodof the present invention, the medium can be read by a computer, and theabove-mentioned program and/or data having been read carry out theabove-mentioned operations in cooperation with the computer.

[0166] Still further, the present invention is a medium that holds aprogram and/or data for carrying out all or part of the functions of allor part of the means of the above-mentioned noise reduction apparatus ofthe present invention, the medium can be read by a computer, and theabove-mentioned program and/or data having been read carry out theabove-mentioned functions in cooperation with the computer.

[0167] Part of the means (or apparatuses, devices, circuits, portions,etc.) of the present invention and part of the steps (or processes,operations, actions, etc.) of the present invention designate some meansor steps in the plural means or steps, or part of functions or part ofactions in one means or step.

[0168] In addition, a recording medium on which the program of thepresent invention has been recorded and which is readable by a computeris also included in the present invention.

[0169] Furthermore, a utilization form of the program of the presentinvention may be an embodiment that is recorded on a recording mediumreadable by a computer and operates in cooperation with the computer.

[0170] Still further, a utilization form of the program of the presentinvention may be an embodiment that is transmitted through atransmission medium and read by a computer and operates in cooperationwith the computer.

[0171] Still further, the data structure of the present inventionincludes a database, a data format, a data table, a data list, a datatype, etc.

[0172] Still further, the recording medium includes ROM, etc., and thetransmission medium includes a transmission medium, such as theInternet, light, electric wave, sound wave, etc.

[0173] Still further, the above-mentioned computer of the presentinvention is not limited to pure hardware, such as a CPU, but mayinclude firmware, an OS and peripheral devices.

[0174] Still further, as described above, the configuration of thepresent invention may be attained by software or by hardware.

[0175] Industrial Applicability

[0176] As described above, the present invention has an effect ofreducing mosquito noise while retaining edges by using simple hardwarewithout using information at the time of compression, such as DCTblocks.

1. A noise reduction method for the decoded signal of a digitallycompressed image signal, comprising: a gradient calculation step ofobtaining a predetermined gradient in an area of vertical M×horizontal Npixels (M and N are positive integers) around a notice pixel, adifference value calculation step of calculating, in an area of verticalJ×horizontal K pixels (J and K are positive integers satisfying therelationships of J≦M and K≦N, respectively) around said notice pixel,(J×K−1) difference values between said notice pixel and pixels otherthan said notice pixel, a correction value calculation step ofcalculating correction values from said gradient obtained by saidgradient calculation step and said (J×K−1) difference values obtained bysaid difference value calculation step, and an addition step ofcalculating a new notice pixel by adding said correction values to saidnotice pixel.
 2. A noise reduction method in accordance with claim 1,wherein said correction value calculation step is a step of calculating(J×K−1) correction values corresponding to the (J×K−1) pixels other thansaid notice pixel, respectively.
 3. A noise reduction method inaccordance with claim 2, wherein said (J×K−1) correction valuescalculated at said correction value calculation step and correspondingto said (J×K−1) pixels other than said notice pixel are calculated sothat, (a−1) each of said correction values becomes larger as each ofsaid (J×K−1) difference values becomes larger until an evaluation valuebased on said predetermined gradient and said difference value exceeds apredetermined threshold value T, and (a−2) each of said correctionvalues holds a constant value or becomes smaller than the constant valueas each of said (J×K−1) difference values becomes larger and when saidevaluation value exceeds said threshold value T, and so that (b−1) asign of said correction value is positive when the pixel value of saidnotice pixel is larger than or equal to the corresponding (J×K−1) pixelvalues, and (b−2) the sign is negative when the pixel value of saidnotice pixel is smaller.
 4. A noise reduction method in accordance withclaim 2, wherein said correction value calculation step carries outcalculation such that, when the absolute value of the result of theaddition of all of said (J×K−1) correction values is larger than apredetermined value L, a correction value having the sign of which isthe same as that of the result of the addition of all of said (J×K−1)values and the predetermined value L, is obtained, and when the absolutevalue is not more than the predetermined value L, the result of theaddition of all of said (J×K−1) values is obtained as said correctionvalue.
 5. A noise reduction method in accordance with claim 1, whereinsaid predetermined gradient calculated by said gradient calculation stepis the maximum value of the difference values of the adjacent pixels insaid area of vertical M×horizontal N pixels.
 6. A noise reduction methodin accordance with claim 5, wherein as said maximum value of saiddifference values becomes larger, said correction values calculated bysaid correction value calculation step become larger.
 7. A noisereduction apparatus for the decoded signal of a digitally compressedimage signal, comprising: gradient calculation means of obtaining apredetermined gradient in an area of vertical M×horizontal N pixels (Mand N are positive integers) around a notice pixel, difference valuecalculation means of calculating, in an area of vertical J×horizontal Kpixels (J and K are positive integers satisfying the relationships ofJ≦M and K≦N, respectively) around said notice pixel, (J×K−1) differencevalues between said notice pixel and pixels other than said noticepixel, correction value calculation means of calculating correctionvalues from said gradient obtained by said gradient calculation meansand said (J×K−1) difference values obtained by said difference valuecalculation means, and addition means of calculating a new notice pixelby adding said correction values to said notice pixel.
 8. A noisereduction apparatus in accordance with claim 7, wherein said correctionvalue calculation means calculates (J×K−1) correction valuescorresponding to the (J×K−1) pixels other than said notice pixel,respectively.
 9. A noise reduction apparatus in accordance with claim 8,wherein said (J×K−1) correction values calculated by said correctionvalue calculation means and corresponding to said (J×K−1) pixels otherthan said notice pixel are calculated so that, (a−1) each of saidcorrection values becomes larger as each of said (J×K−1) differencevalues becomes larger until an evaluation value based on saidpredetermined gradient and said difference value exceeds a predeterminedthreshold value T, and (a−2) each of said correction values holds aconstant value or becomes smaller than the constant value as each ofsaid (J×K−1) difference values becomes larger and when said evaluationvalue exceeds said threshold value T, and so that (b−1) a sign of saidcorrection value is positive when the pixel value of said notice pixelis larger than or equal to the corresponding (J×K−1) pixel values, and(b−2) the sign is negative when the pixel value of said notice pixel issmaller.
 10. A noise reduction apparatus in accordance with claim 8,wherein said correction value calculation means carries out calculationsuch that, when the absolute value of the result of the addition of allof said (J×K−1) correction values is larger than a predetermined valueL, the correction value having the sign of which is the same as that ofthe result of the addition of all of said (J×K−1) values and thepredetermined value L, is obtained, and when the absolute value is notmore than the predetermined value L, the result of the addition of allof said (J×K−1) values is obtained as said correction value.
 11. A noisereduction apparatus in accordance with claim 8, wherein said (J×K−1)correction values are read from (J×K−1) memory devices, respectively.12. A noise reduction apparatus in accordance with claim 11, whereincontents to be held in said memory devices are rewritable depending oninputs.
 13. A noise reduction apparatus for the decoded signal of adigitally compressed image signal, comprising: gradient calculationmeans of obtaining a predetermined gradient in an area of verticalM×horizontal N pixels (M and N are positive integers) around a noticepixel, difference value calculation means of calculating, in an area ofvertical J×horizontal K pixels (J and K are positive integers satisfyingthe relationships of J<=M and K<=N, respectively) around said noticepixel, (J×K−1) difference values between said notice pixel and pixelsother than said notice pixel, filter coefficient calculation means ofcalculating filter coefficient from said gradient obtained by saidgradient calculation means and said (J×K−1) difference values obtainedby said difference value calculation means, and filtering means ofcarrying out filtering on the basis of said calculated filtercoefficients.
 14. A noise reduction apparatus in accordance with claim13, wherein said filter coefficient calculation means calculates (J×K−1)filter coefficients corresponding to the (J×K−1) pixels other than saidnotice pixel, respectively.
 15. A noise reduction apparatus inaccordance with claim 14, wherein said (J×K−1) filter coefficientscalculated by said filter coefficient calculation means andcorresponding to said (J×K−1) pixels other than said notice pixel areobtained by carrying out predetermined calculations from the candidatesof filter coefficients, (a−1) each of which holds a constant value orbecomes larger as the gradient in said area of M×N becomes larger, and(a−2) each of which holds a constant value or becomes smaller as each ofsaid (J×K−1) difference values becomes larger, and (b) the filtercoefficient of said notice pixel is determined so that the sum of thefilter coefficient of said notice pixel and said (J×K−1) filtercoefficients of said pixels other than said notice pixel becomes one.16. A noise reduction apparatus in accordance with claim 15, whereinsaid predetermined calculation is a calculation for carrying outclassification depending on the distances of the pixels corresponding tosaid filter coefficient candidates from said notice pixel and forcarrying out correction so that the filter coefficients of pixels awayfrom said notice pixel become smaller than any filter coefficients ofpixels near said notice pixel
 17. A noise reduction apparatus inaccordance with claim 14, wherein said (J×K−1) filter coefficients areread from (J×K−1) memory devices, respectively.
 18. A noise reductionapparatus in accordance with claim 17, wherein contents to be held insaid memory devices are rewritable depending on inputs.
 19. A mediumholding a program and/or data for carrying out the operations of all orpart of the steps of said noise reduction method in accordance with anyone of claims 1 to 6 by using a computer and being processable by thecomputer.
 20. A medium holding a program and/or data for carrying outthe functions of all or part of the means of said noise reductionapparatus in accordance with any one of claims 7 to 18 by using acomputer and being processable by the computer.
 21. A program forcausing a computer to carry out all or part of said gradient calculationstep, said difference value calculation step, said correction valuecalculation step and said addition step of said noise reductionapparatus in accordance with any one of claims 1 to
 6. 22. A program foractivating a computer as all or part of said gradient calculation means,said difference value calculation means, said correction valuecalculation means and said addition means of said noise reductionapparatus in accordance with any one of claims 7 to 18.